It is well known that an oscillating element set into motion by the vibration produced on striking the ball, e.g. against the stringing of a tennis racket has the effect of attenuating vibration thereof. The oscillating element or device is preferably placed in the vicinity of a vibration antinode of the racket. The self-damped oscillating device picks up the vibration and is set into motion, thereby releasing vibrational energy. However, in addition to the fact that they need to be included in the instrument during manufacture, such devices present a projecting oscillating portion that can impede the handling of said instrument by the player. When the handle of the instrument is hollow, it is indeed possible to place the oscillating device inside the handle, but in that case its travel is limited by the inside diameter of the handle, thereby limiting its effectiveness. No presently known device completely absorbs the vibration of a ball-game instrument without also having a projection that can hinder the hand of the player during play.